Try below PowerShell.
$web = Get-SPWeb -site https://webapp.domain.com/sites/sitecollection
foreach($web in $web.Webs){
$lists = $web.Lists | Where-Object { $_.Title -eq 'CustomList1' }
$choice = $lists.fields | Where-Object { $_.Title -eq 'ChoiceColumn1' }
$choice.choices
$choice.choices.add("New Value")
$choice.update()
}
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